PHILOSOPHICAL SOCIETY OF WASHINGTON. 59 



The equations which Le Verrier uses in his theories of the planets 

 are not as simple in form as those of Delaunay ; but there is no 

 difficulty attending their derivation by this method. The method 

 Le Verrier uses in deriving them is long and cumbrous. Delaunay 

 does not stop to derive the equations he uses, but refers, on this 

 head, to a memoir by Benet. 



By the method given above I have derived all the fundamental 

 equations used by these authors, and by those who have considered 

 the subject of perturbations from the same standpoint. 



I think I have here given enough of the j>rocess to enable any 

 one to understand the method. I may add that the method occurred 

 to me seven or eight years ago. 



The next communication was by Mr. Edgar Frisby 



ON THE ORBIT OF SWIFT'S COMET. 



This comet was first observed by Prof. Swift of Rochester, Oc- 

 tober 10, 1880, and was reported by him as moving directly towards 

 the earth. It was observed by Prof. Eastman with the transit cir- 

 cle of the U. S. Naval Observatory on the evenings of October 25, 

 November 7, and November 20, and from the data so obtained the 

 following elements were computed by Prof. Frisby : 



Epoch of perihelion passage 7 d .775675 Washington mean time 



Q = 296° 48' 19. "9 1 



77 = 42° 59' 15. "8 



& = 42° 26' 48. "5 



i = 5° 30' 35. "9 



log a = 0.517002 



\og fi= 2.774504 J 



Mean Equinox 1880.0. 



From these elements it will be inferred that it was moving very 

 nearly towards the earth at the time of discovery, October 10. On 

 November 8, it came very near the earth's orbit, its distance from it 

 then being about 0.069 of the earth's mean distance from the sun. 

 The aphelion lies just beyond Jupiter's orbit so that its perturbations 

 are liable at any time to become immense. The periodic time from 

 the elements is about 2,178 days, or a little less than six years, 

 but Jupiter's position in his orbit is now such that it is not likely 

 to come near the comet for a long period. For a time after the 

 discovery of the comet it was doubtful whether the period was 11 

 or 5£ years. The latter is undoubtedly the true one, the slight 



